The Exact Controllability Property of Neutral Type Systems by the Moment Problem Approach Revisited

Rabah Rabah (1) , Grigory M. Sklyar (2) , Pavel Yu. Barkhayev (3)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 Institute of Mathematics, University of Szczecin
3 Department of Differential Equations and Control, Kharkov National University

In a recent paper authors gave an analysis of the exact controllability problem via the moment problem approach. Namely, the steering conditions of controllable states are formulated as a vectorial moment problem using some Riesz basis. One of the main difficulties was the choice of the basis as, in general, a basis of eigenvectors does not exist. In this contribution we use a change of control by a feedback law and modify the structure of the system in such a way that there exists a basis of eigenvectors which allows a simpler expression of the moment problem. Hence, one obtains the result on exact controllability and on the time of exact controllability.

Mots clés: distributed delays; Neutral-type systems; exact controllability; moment problem; Riesz basis; distributed delays.

Domaines: Optimisation et contrôle [math.OC]; Systèmes dynamiques [math.DS]

Rabah Rabah, Grigory M. Sklyar, Pavel Yu. Barkhayev. The Exact Controllability Property of Neutral Type Systems by the Moment Problem Approach Revisited. 9th IFAC Workshop on Time Delay Systems, Jun 2010, Prague, Czech Republic. pp. 171--176, ⟨10.3182/20100607-3-CZ-4010.00032⟩. ⟨hal-00465056⟩